• Dr. Umesh Vaidya
  • Iowa State University
  • Holden Auditorium
  • 4:00 p.m.

Analysis and control of uncertain nonlinear systems exhibiting non-equilibrium dynamics is of interest in various applications such as fluid flow control, control of complex networks, and biological systems. In this talk we present
results on the novel ergodic theory-based framework for the analysis and control of non-equilibrium dynamics in uncertain dynamical systems. Our first main result is on the introduction of Lyapunov measure as a new tool for stability verification and stabilization of non-equilibrium dynamics in nonlinear systems. The main contribution of this work is that it provides for a systematic linear programming based solution for the stability verification and stabilization of non-equilibrium dynamics in nonlinear systems. The novel framework is also used to study the problems of stabilization and estimation of nonlinear systems over uncertain channels and interconnections. We show that fundamental limitations arise in the stabilization and estimation of nonlinear systems over uncertain channels, expressed in terms of variance of channel uncertainty and system instability. The main contribution of this work is that it highlights, for the first time, the important role-played by the global non-equilibrium dynamics in obtaining the limitation results. The framework is extendable to study more general control problems over uncertain networks with nonlinear components dynamics.